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A unified approach to pricing and risk management of equity and credit risk

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  • Claudio Fontana
  • Juan Miguel A. Montes
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    Abstract

    We propose a unified framework for equity and credit risk modeling, where the default time is a doubly stochastic random time with intensity driven by an underlying affine factor process. This approach allows for flexible interactions between the defaultable stock price, its stochastic volatility and the default intensity, while maintaining full analytical tractability. We characterise all risk-neutral measures which preserve the affine structure of the model and show that risk management as well as pricing problems can be dealt with efficiently by shifting to suitable survival measures. As an example, we consider a jump-to-default extension of the Heston stochastic volatility model.

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    File URL: http://arxiv.org/pdf/1212.5395
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1212.5395.

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    Date of creation: Dec 2012
    Date of revision: May 2013
    Publication status: Published in Journal of Computational and Applied Mathematics (2014), vol. 259, pp. 350-261
    Handle: RePEc:arx:papers:1212.5395

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    Web page: http://arxiv.org/

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    1. Peter Carr & Wim Schoutens, 2008. "Hedging Under The Heston Model With Jump-To-Default," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 403-414.
    2. E. Bayraktar, 2008. "Pricing Options on Defaultable Stocks," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 277-304.
    3. Joost Driessen, 2005. "Is Default Event Risk Priced in Corporate Bonds?," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 165-195.
    4. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    5. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    7. Rehez Ahlip & Marek Rutkowski, 2009. "Forward Start Options Under Stochastic Volatility And Stochastic Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 209-225.
    8. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.
    9. Delia Coculescu & Monique Jeanblanc & Ashkan Nikeghbali, 2012. "Default times, no-arbitrage conditions and changes of probability measures," Finance and Stochastics, Springer, vol. 16(3), pages 513-535, July.
    10. Campbell, John & Taksler, Glen, 2003. "Equity Volatility and Corporate Bond Yields," Scholarly Articles 3153307, Harvard University Department of Economics.
    11. Gregory R. Duffee, 1996. "Estimating the price of default risk," Finance and Economics Discussion Series 96-29, Board of Governors of the Federal Reserve System (U.S.).
    12. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Economics Papers from University Paris Dauphine 123456789/409, Paris Dauphine University.
    13. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
    14. Peter Carr & Liuren Wu, 2010. "Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 409-449, Fall.
    15. Martijn Cremers & Joost Driessen & Pascal Maenhout & David Weinbaum, 2004. "Individual Stock-Option Prices and Credit Spreads," Yale School of Management Working Papers amz2391, Yale School of Management, revised 01 Jan 2005.
    16. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
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